Question

graph the line that has a slope of \\(\frac{1}{6}\\) and includes the point (0, 0). click to select points on the graph. graph with x-axis from 0 to 10 and y-axis from 0 to 10, grid lines present

Explanation:

Step1: Recall the slope formula

The slope \( m \) is defined as \( m = \frac{\text{rise}}{\text{run}} \), where rise is the change in \( y \) and run is the change in \( x \). Given \( m = \frac{1}{6} \), this means for every 6 units we move to the right (run = 6) on the \( x \)-axis, we move up 1 unit (rise = 1) on the \( y \)-axis.

Step2: Identify the starting point

The line passes through \( (0, 0) \), so this is our first point.

Step3: Find the next point

Using the slope, from \( (0, 0) \), move 6 units to the right (increase \( x \) by 6: \( 0 + 6 = 6 \)) and 1 unit up (increase \( y \) by 1: \( 0 + 1 = 1 \)). So the next point is \( (6, 1) \). We can also move in the opposite direction: from \( (0, 0) \), move 6 units left ( \( x = 0 - 6 = -6 \)) and 1 unit down ( \( y = 0 - 1 = -1 \)), but since the graph shows \( x \) and \( y \) from 0 to 10 (and 0 to 1 for \( y \) in the lower range), \( (6, 1) \) is a visible point on the given grid.

Step4: Draw the line

Plot the points \( (0, 0) \) and \( (6, 1) \) (and other points using the slope if needed) and draw a straight line through them.

Answer:

To graph the line, plot the point \((0, 0)\) (the origin) and then use the slope \(\frac{1}{6}\) to find another point: from \((0, 0)\), move 6 units right (to \(x = 6\)) and 1 unit up (to \(y = 1\)) to get \((6, 1)\). Draw a straight line through \((0, 0)\) and \((6, 1)\) (and extend it as needed). The key points to plot are \((0, 0)\) and \((6, 1)\) (among others following the slope).